Moments and pi-electron energy of hexagonal systems in 3-space

Abstract

Let G be a finite hexagonal system with boundary embedded in the 3-dimensional space. We consider the dependence of the spectral moments M-k(G) and the total pi-electron energy E-pi(G) on the molecular structure of G. Our formulas involve the classical structural invariants of G and the rank of the fundamental group pi(1)(G), which is a (non-abelian) free group. Our results generalize the benzenoid formulas (where pi(1) (G) = 0).